FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 3, PAGES 927-935

V. K. Zakharov

A. V. Mikhalev

Abstract

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In the first volume of the treatise ``\'El\'ements de math\'ematique''\
Bourbaki has given one of possible rigorous definitions of
a \emph{mathematical structure}.
However, it turned out that this definition is not much suitable
for broad usage, because structures in Bourbaki's sense possess
considerable bracket partition, which means the definite order of priority
in assignment of constituent partial structures (such as addition, order,
norm, topology, measure, etc.).
```

In this paper a \emph{conception of a mathematical system} is presented,
which includes as partial cases both the bracket conception of
a mathematical structure in Bourbaki's sense and the bracket-free
conception of an algebraic system in Birkhoff--Tarski's sense,
and which enables in particular to construct corresponding bracket-free
structures for many important mathematical systems.

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Last modified: December 15, 1998